Add warm coconut milk to bowl of stand mixer with the dough hook attached. Add yeast and 1 tbsp of sugar and gently stir. Let sit until foamy, approx. 10 minutes.
Add remaining sugar, melted coconut oil, vanilla extract, and egg. Whisk to combine. Add flour, cinnamon, nutmeg, and salt. Knead with dough hook until dough forms a smooth ball. Note: you may have to stop periodically and use a spatula to scrap sides of the bowl. Remove dough from bowl and knead with hands for 1-2 minutes. Spray bowl with cooking spray. Add dough back to the bowl and cover with plastic wrap. Let dough sit for 2 hours or until dough doubles in size.
While the dough is rising, make the filling. Combine cinnamon, sugar, butter, ginger, and nutmeg to a clean bowl and mix until batter forms a paste.
Once dough rises, roll the dough into a 12 x 24 in rectangle on a floured surface. Spread the cinnamon sugar paste onto the dough. Sprinkle desiccated coconut on top of the filling. Carefully roll the dough into a log, making sure to roll the dough tightly. Use a sharp knife to cut the dough into 10-12 even rolls.
Grease a 9 x 13 baking tin. Place rolls on the baking tin and cover with a warm, damp towel until the dough doubles in size (about 30 minutes).
Preheat oven to 350 degrees. Remove towel and bake rolls for 20-25 minutes, or until golden brown.
While the rolls are baking, make the ginger cream cheese filling by creaming butter, cream cheese, and powdered sugar in a mixing bowl on low speed (use the whisk attachment). Add ginger, nutmeg, and vanilla extract and mix until the frosting is fluffy and well combined. Keep at room temperature until rolls are done baking.
Remove rolls from the oven. Spread frosting onto warm rolls and let the rolls cool. Enjoy!